I'm an IT-student and writing a thesis about atomic swaps on BTC and BTC-like blockchains. For the thesis I decided to use BTC, LTC, BCH and DCR. These chains have a somehow similar codebase and the same scripting language (I'm not a professional, so there might be differences, but they are not that serious). And they all have a high enough marketcap to be relevant for atomic swaps.So the goal of the thesis is to find hashed timelock contracts (HTLCs) and connect matching HTLCs from different chains to get the atomic swap. Therefore I first searched the web for anything on atomic swaps [1] and analyzed the input script of this transaction [2] to get a basic understanding how atomic swaps work and what they look like.Then I wrote a go program to search for any script longer than simple P2PKH scripts. This gave me a list of many different scripts which I analyzed by hand to only take the HTLC ones. (Besides many multisig scripts, there is not much to find on BTC^^)At this point I found multiple different types of HTLCs as listed below. Afterwards I crawled* BTC again saving all transactions with HTLC scripts, storing the interesting data like tx-id, input value, pubKeyHashes, the secrets and their hashes. I found about one hundret HTLCs on BTC so far.I did the same for LTC and found about 400 HTLCs.As far as I understood, the secrets of HTLCs have to be the same on both chains. So I wrote another go program to match the found HTLCs from BTC and LTC and got around 30 matches. The next steps would then be to crawl BCH and DCR and also match the HTLCs found there.

* Crawling in this case means that I start to search the blockchain backwards (to get the newest first, the beginning years are not that interesting in this case^^) until the beginning of 2017. So about 18 months. As stated in [1] the first known atomic swap between BTC and LTC was made on 19th April 2017 (or April 19th 2017 or 19.4.2017 or whatever you like). So there is not much sense in crawling any further.

My questions now are the following:

Why are there so many different types? Is it compatibility with other chains? Or what?

What are the differences between these types (besides length and hashing algorithm)?

What are the advantages and disadvantages of these types?

Why are there so many HTLCs on LTC and so few on BTC?

Do you know other such HTLC scripts?

Can you provide interesting resources on this topic?

I'm open to any constructive input and hope you have a few answers for me. Thank you in advance.

Lightning Network uses HTLCs as fundamental building blocks, so maybe this accounts for some of the HTLCs you are seeing that do not correlate to atomic cross-chain swaps? The first known mainnet LN transaction took place some time in late December 2017 [1] so that should be the first time that a LN related HTLC hit the blockchain. However there are currently more than 6000 LN channels open [2] so maybe LN opening / closing transaction don't satisfy your search criteria and thus don't show up in the first place.

Why are there so many different types? Is it compatibility with other chains? Or what?

Different implementations of the same idea

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What are the differences between these types (besides length and hashing algorithm)?

Type 1 stands out by its first instructions, ensuring the supplied secret preimage to the puzzle hash is 32 (0x20) bytes in length. It's there to mitigate the attack described here: https://gist.github.com/markblundeberg

Type 2a appears to be broken, couldn't figure this one out. It tries to compare hash160(puzzle_hash) == pubkey_hash1, with both values in the same script, which doesn't make sense.

Type 2b is the most straightforward. If sha256 of preimage matches the hash and signed by Bob, or timelock is unlocked and signed by Alice, allow to spend the output.

Type 4a just swaps the conditions, which doesn't affect anything (except the switch value you put that will decide which branch of OP_IF will be executed). Plus, as in Type 1, it puts constraints on the secret preimage's size. You got the labels here wrong, by the way, <secret_hash 20byte> and <pubkey_hash1 20byte> should be swapped.

Type 4b is the same as 4a, minus the size check.

Type 5a uses CHECKSEQUENCEVERIFY instead of CHECKLOCKTIMEVERIFY, which is a minor difference. If you're at block 500, and you want to lock the coins until block 530, you can either say "530 CHECKLOCKTIMEVERIFY" or "30 CHECKSEQUENCEVERIFY" (I might have made an off-by-one error here though, check the BIP for the exact usage).

Type 5b: the only difference with 5a is timelock value size (instead of 4 byte integer, you can have it in a more compact form with only 1 byte integer, which will give you a lock period of up to 256 blocks).

Type 6: is exactly like Type 4b, only it uses a shorthand for pushing the timelock value. You also got the labels backwards here, swap <secret_hash> with <pubkey_hash1>.

Type 7 and 8: as you correctly noticed, they use several puzzles at once. Got no idea why. Maybe it has something to do with the puzzle datatype size constraints on the altcoin side of the exchange.

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What are the advantages and disadvantages of these types?

They appear to be slight modifications of each other, primarily on the order of conditions, sometimes with additional verifications to avoid certain types of attacks.

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Why are there so many HTLCs on LTC and so few on BTC?

LTC block time is much less than BTC's. Since atomic swaps is still an experimental technology, it makes sense to test them on a faster chain, paired with some other altcoin having the comparatively fast block time.

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Do you know other such HTLC scripts?

Well, you scanned the whole blockchain, have you found any other type yet?

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Can you provide interesting resources on this topic?

My advice would be to learn how to read Bitcoin scripts, that way you will be able to understand what they do and how they compare to each other. You can start here: https://en.bitcoin.it/wiki/Script, or you can go deep into the guts of interpreter.cpp, where the actual magic happens.